Practice section 8 of 8

(a) Mrs Wang bakes 15 chocolate and 25 blueberry cupcakes, then gives away 8 chosen at random. Find the probability exactly 3 are chocolate. [2]

(b) In a seasonal-flu exercise, the probability a person receives a flu vaccine is 0.85. The probability of flu is 0.23 given vaccination and 0.91 given no vaccination. Find the probability that

(i) a person gets flu, [2]

(ii) of two randomly chosen people who got flu, exactly one received the vaccine. [3]

p% of students take Mathematics A and the remaining(100−p)% take Mathematics B.30% of Math A students fail and 40% of Math B students fail.

(i) Show that the probability exactly one of two students fails is $0.0002(2400-2p-0.01p^2)$. [5]

(ii) Given the probability both take Math A, conditional on exactly one failing, is $7/48$, find p. [3]

A set of 40 cards is assembled from several ordinary packs, with counts:

Rank	Spades	Hearts	Diamonds	Clubs
King	3	2	6	4
Queen	4	5	4	1
Jack	1	3	2	5

For example, there are 4 Kings of Clubs and 3 Jacks of Hearts. Three cards are drawn at random without replacement.

(i) Find the probability they are three Kings, three Queens or three Jacks. [3]

(ii) Given two Spades and one Diamond are drawn, find the probability they are three Kings, three Queens or three Jacks. For example, two Kings of Spades and one King of Diamonds qualify. [4]